The legal situation here is interesting. The costs of a successful rescue are relatively insignificant compared to potential damages for injury. But it does appear that the law is reasonably sensible.
The common law principle of sovereign immunity means that you generally can’t sue the government; but the Federal Tort Claims Act is a limited waiver of this immunity that might in principle allow you to sue (for example) the National Park Service for negligence if you got injured. This would obviously have disastrous consequences, requiring extremely conservative safety policies from federal agencies who oversee public lands - do we want 8 foot barbed wire fencing all along the rim of the Grand Canyon? However, most states have recreational use statutes to encourage private landowners to provide public access to their land without risk of liability, and I think this is what protects federal agencies - the FTCA waiver only applies if a private individual would be liable.
On the other hand, it’s not unusual for injured rescuers to sue anyone who may have contributed to creating the need for rescue, including potentially the person rescued.
IANAL, but I think if one of the rescuers had been injured in this situation, they would have a decent case for suing the idiot who recklessly crossed the barrier.